The Schrödinger-Poisson-Xα equation

We deal with the inclusion of exchange effects in the self-consistent one particle Schrödinger equation. For the stationary case local approximations (of the Hartree-Fock equations) can be rigorously justified. By heuristically using these terms in the time dependent case we add the local exchange p...

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Bibliographic Details
Published in:Applied mathematics letters 2001-08, Vol.14 (6), p.759-763
Main Author: Mauser, N.J.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fock equations
Hartree
Mathematics
Nonlinear Schrödinger equations
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Sciences and techniques of general use
Semiconductor modeling
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Summary:We deal with the inclusion of exchange effects in the self-consistent one particle Schrödinger equation. For the stationary case local approximations (of the Hartree-Fock equations) can be rigorously justified. By heuristically using these terms in the time dependent case we add the local exchange potential of the Xα method to the Hartree equations. Thus, we obtain the “Schrödinger-Poisson- Xα” model where the effective potential is the difference of the nonlocal Coulomb potential and the third root of the local density.
ISSN:0893-9659
1873-5452
DOI:10.1016/S0893-9659(01)80038-0